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PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361019 A cube made of material having a density of $0.9 \times 10^{3} k g m^{- 3}$ floats between water and a liquid of density $0.7 \times 10^{3} k g m^{- 3}$ which is immisicible with water. what part of the cube is immersed in water?

1

\frac{1}{3}

2

\frac{2}{3}

3

\frac{3}{4}

4

\frac{3}{7}

Explanation:

Let $l =$ side of the cube,
$x =$ side of cube immersed in water
and $l - x =$ side of cube immersed in liquid.
According to law of floatation,
$\begin{array}{r} l^{3} \times 0.9 \times 10^{3} \times g = (l^{2} \times x) \times 1000 g \\ + l^{2} (l - x) \times 0.7 \times 10^{3} g \\ [∵ V_{1} ρ_{1} g = V_{2} ρ_{2} g] \\ \Rightarrow l \times 0.9 = x + (l - x) \times 0.7 \end{array}$
or $0.3 x = 0.2 l$ or $\frac{x}{l} = \frac{2}{3}$

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361020 A solid uniform cylindrical object of diameter $20 c m$ and mass $2 k g$ floats in water with its axis vertical. If it is depressed by $4 c m$ and released, the initial acceleration of the cylinder is $n π m / s^{2}$ , Find the value of $n (g = 10 m / s^{2})$

1 3

2 2

3 4

4 1

Explanation:

When the cylinder is floating in liquid its downward weight is balanced by buoyancy force. When the cylinder is depressed further then buoyancy force increases. The increase in buoyancy force will produce acceleration.
$Δ F_{b} = m a$
$ρ_{l} A Δ y g = 2 a$
$a = \frac{10^{3} \times π \times {(0.1)}^{2} \times 0.04 \times 10}{2} m / s^{2} = 2 π m / s^{2}$
$∴ n = 2$

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361021 For a body immersed in a liquid, when the weight of the body is less than the upthrust, then the body will

1 Sink

2 Float partially immersed

3 Be of zero weight

4 Float full immersed

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361022 A cubical block of wood $10 c m$ on a side, floats at the interface of oil and water as shown in figure. The density of oil is $0.6 g c m^{- 3}$ and density of water is $1 g c m^{- 3}$ . The mass of the block is
supporting img

1

607 g

2

706 g

3

670 g

4

760 g

Explanation:

$m = \frac{F_{b_{1}} + F_{b_{2}}}{g}$
$m = 10^{2} \times 6 \times 0.6 + 10^{2} \times 4 \times 1 = 760 g$

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361019 A cube made of material having a density of $0.9 \times 10^{3} k g m^{- 3}$ floats between water and a liquid of density $0.7 \times 10^{3} k g m^{- 3}$ which is immisicible with water. what part of the cube is immersed in water?

1

\frac{1}{3}

2

\frac{2}{3}

3

\frac{3}{4}

4

\frac{3}{7}

Explanation:

Let $l =$ side of the cube,
$x =$ side of cube immersed in water
and $l - x =$ side of cube immersed in liquid.
According to law of floatation,
$\begin{array}{r} l^{3} \times 0.9 \times 10^{3} \times g = (l^{2} \times x) \times 1000 g \\ + l^{2} (l - x) \times 0.7 \times 10^{3} g \\ [∵ V_{1} ρ_{1} g = V_{2} ρ_{2} g] \\ \Rightarrow l \times 0.9 = x + (l - x) \times 0.7 \end{array}$
or $0.3 x = 0.2 l$ or $\frac{x}{l} = \frac{2}{3}$

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361020 A solid uniform cylindrical object of diameter $20 c m$ and mass $2 k g$ floats in water with its axis vertical. If it is depressed by $4 c m$ and released, the initial acceleration of the cylinder is $n π m / s^{2}$ , Find the value of $n (g = 10 m / s^{2})$

1 3

2 2

3 4

4 1

Explanation:

When the cylinder is floating in liquid its downward weight is balanced by buoyancy force. When the cylinder is depressed further then buoyancy force increases. The increase in buoyancy force will produce acceleration.
$Δ F_{b} = m a$
$ρ_{l} A Δ y g = 2 a$
$a = \frac{10^{3} \times π \times {(0.1)}^{2} \times 0.04 \times 10}{2} m / s^{2} = 2 π m / s^{2}$
$∴ n = 2$

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361021 For a body immersed in a liquid, when the weight of the body is less than the upthrust, then the body will

1 Sink

2 Float partially immersed

3 Be of zero weight

4 Float full immersed

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361022 A cubical block of wood $10 c m$ on a side, floats at the interface of oil and water as shown in figure. The density of oil is $0.6 g c m^{- 3}$ and density of water is $1 g c m^{- 3}$ . The mass of the block is
supporting img

1

607 g

2

706 g

3

670 g

4

760 g

Explanation:

$m = \frac{F_{b_{1}} + F_{b_{2}}}{g}$
$m = 10^{2} \times 6 \times 0.6 + 10^{2} \times 4 \times 1 = 760 g$

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361019 A cube made of material having a density of $0.9 \times 10^{3} k g m^{- 3}$ floats between water and a liquid of density $0.7 \times 10^{3} k g m^{- 3}$ which is immisicible with water. what part of the cube is immersed in water?

1

\frac{1}{3}

2

\frac{2}{3}

3

\frac{3}{4}

4

\frac{3}{7}

Explanation:

Let $l =$ side of the cube,
$x =$ side of cube immersed in water
and $l - x =$ side of cube immersed in liquid.
According to law of floatation,
$\begin{array}{r} l^{3} \times 0.9 \times 10^{3} \times g = (l^{2} \times x) \times 1000 g \\ + l^{2} (l - x) \times 0.7 \times 10^{3} g \\ [∵ V_{1} ρ_{1} g = V_{2} ρ_{2} g] \\ \Rightarrow l \times 0.9 = x + (l - x) \times 0.7 \end{array}$
or $0.3 x = 0.2 l$ or $\frac{x}{l} = \frac{2}{3}$

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361020 A solid uniform cylindrical object of diameter $20 c m$ and mass $2 k g$ floats in water with its axis vertical. If it is depressed by $4 c m$ and released, the initial acceleration of the cylinder is $n π m / s^{2}$ , Find the value of $n (g = 10 m / s^{2})$

1 3

2 2

3 4

4 1

Explanation:

When the cylinder is floating in liquid its downward weight is balanced by buoyancy force. When the cylinder is depressed further then buoyancy force increases. The increase in buoyancy force will produce acceleration.
$Δ F_{b} = m a$
$ρ_{l} A Δ y g = 2 a$
$a = \frac{10^{3} \times π \times {(0.1)}^{2} \times 0.04 \times 10}{2} m / s^{2} = 2 π m / s^{2}$
$∴ n = 2$

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361021 For a body immersed in a liquid, when the weight of the body is less than the upthrust, then the body will

1 Sink

2 Float partially immersed

3 Be of zero weight

4 Float full immersed

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361022 A cubical block of wood $10 c m$ on a side, floats at the interface of oil and water as shown in figure. The density of oil is $0.6 g c m^{- 3}$ and density of water is $1 g c m^{- 3}$ . The mass of the block is
supporting img

1

607 g

2

706 g

3

670 g

4

760 g

Explanation:

$m = \frac{F_{b_{1}} + F_{b_{2}}}{g}$
$m = 10^{2} \times 6 \times 0.6 + 10^{2} \times 4 \times 1 = 760 g$

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361019 A cube made of material having a density of $0.9 \times 10^{3} k g m^{- 3}$ floats between water and a liquid of density $0.7 \times 10^{3} k g m^{- 3}$ which is immisicible with water. what part of the cube is immersed in water?

1

\frac{1}{3}

2

\frac{2}{3}

3

\frac{3}{4}

4

\frac{3}{7}

Explanation:

Let $l =$ side of the cube,
$x =$ side of cube immersed in water
and $l - x =$ side of cube immersed in liquid.
According to law of floatation,
$\begin{array}{r} l^{3} \times 0.9 \times 10^{3} \times g = (l^{2} \times x) \times 1000 g \\ + l^{2} (l - x) \times 0.7 \times 10^{3} g \\ [∵ V_{1} ρ_{1} g = V_{2} ρ_{2} g] \\ \Rightarrow l \times 0.9 = x + (l - x) \times 0.7 \end{array}$
or $0.3 x = 0.2 l$ or $\frac{x}{l} = \frac{2}{3}$

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361020 A solid uniform cylindrical object of diameter $20 c m$ and mass $2 k g$ floats in water with its axis vertical. If it is depressed by $4 c m$ and released, the initial acceleration of the cylinder is $n π m / s^{2}$ , Find the value of $n (g = 10 m / s^{2})$

1 3

2 2

3 4

4 1

Explanation:

When the cylinder is floating in liquid its downward weight is balanced by buoyancy force. When the cylinder is depressed further then buoyancy force increases. The increase in buoyancy force will produce acceleration.
$Δ F_{b} = m a$
$ρ_{l} A Δ y g = 2 a$
$a = \frac{10^{3} \times π \times {(0.1)}^{2} \times 0.04 \times 10}{2} m / s^{2} = 2 π m / s^{2}$
$∴ n = 2$

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361021 For a body immersed in a liquid, when the weight of the body is less than the upthrust, then the body will

1 Sink

2 Float partially immersed

3 Be of zero weight

4 Float full immersed

PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361022 A cubical block of wood $10 c m$ on a side, floats at the interface of oil and water as shown in figure. The density of oil is $0.6 g c m^{- 3}$ and density of water is $1 g c m^{- 3}$ . The mass of the block is
supporting img

1

607 g

2

706 g

3

670 g

4

760 g

Explanation:

$m = \frac{F_{b_{1}} + F_{b_{2}}}{g}$
$m = 10^{2} \times 6 \times 0.6 + 10^{2} \times 4 \times 1 = 760 g$

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